Question

The electric field in a region is radially outward with magnitude $E=r^2+2$. The charge contained in a sphere of radius a = 2 m centred at the origin is $16\pi {\epsilon }_{0}x$. Find the value of x. ___

Answer 1

$\frac{Q}{{\epsilon }_0}=E.S$
$\frac{16\pi {\epsilon }_{0}x}{{\epsilon }_0}=(r^2+2)\left(4\pi r^2\right)$
$4x=\left(6\right)\left(4\right)$
$x=6$